I would like to offer a slightly less confusing explanation of why we have a natural born citizen requirement.
It is not where one is born, but where his allegiances may lie. The NBC requires both parents to be U.S. citizens at the time of a child's birth. A president, who is commander in chief of the U.S. military, cannot have any questionable allegiances through the nationality of one of his parents.
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Most legal disputes have the incorrect evidence of WHERE one is born, rather than WHO the parents are.